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By the end of this section, you will be able to:
  • Use the simple interest formula
  • Solve simple interest applications

Before you get started, take this readiness quiz.

  1. Solve 0.6 y = 45 .
    If you missed this problem, review Decimals and Fractions .
  2. Solve n 1.45 = 4.6 .
    If you missed this problem, review Decimals and Fractions .

Use the simple interest formula

Do you know that banks pay you to let them keep your money? The money you put in the bank is called the principal , P , and the bank pays you interest , I . The interest is computed as a certain percent of the principal; called the rate of interest , r . The rate of interest is usually expressed as a percent per year, and is calculated by using the decimal equivalent of the percent. The variable for time, t , represents the number of years the money is left in the account.

Simple interest

If an amount of money, P , the principal, is invested for a period of t years at an annual interest rate r , the amount of interest, I , earned is

I = P r t

where

I = interest P = principal r = rate t = time

Interest earned according to this formula is called simple interest    .

The formula we use to calculate simple interest is I = P r t . To use the simple interest formula we substitute in the values for variables that are given, and then solve for the unknown variable. It may be helpful to organize the information by listing all four variables and filling in the given information.

Find the simple interest earned after 3 years on $500 at an interest rate of 6%.

Solution

Organize the given information in a list.

I = ? P = $500 r = 6% t = 3 years

We will use the simple interest formula to find the interest.

Write the formula. I = P r t
Substitute the given information. Remember to write the percent in decimal form. I = ( 500 ) ( 0.06 ) ( 3 )
Simplify. I = 90
Check your answer. Is $90 a reasonable interest earned on $500 in 3 years?
In 3 years the money earned 18%. If we rounded to 20%, the interest would have been 500(0.20) or $100. Yes, $90 is reasonable.
Write a complete sentence that answers the question. The simple interest is $90.
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Find the simple interest earned after 4 years on $800 at an interest rate of 5%.

$160

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Find the simple interest earned after 2 years on $700 at an interest rate of 4%.

$56

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In the next example, we will use the simple interest formula to find the principal.

Find the principal invested if $178 interest was earned in 2 years at an interest rate of 4%.

Solution

Organize the given information in a list.

I = $178 P = ? r = 4% t = 2 years

We will use the simple interest formula to find the principal.

Write the formula. I = P r t
Substitute the given information. 178 = P ( 0.04 ) ( 2 )
Divide. 178 0.08 = 0.08 P 0.08
Simplify. 2,225 = P
Check your answer. Is it reasonable that $2,225 would earn $178 in 2 years?
I = P r t
178 = ? 2,225 ( 0.04 ) ( 2 )
178 = 178
Write a complete sentence that answers the question. The principal is $2,225.
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Find the principal invested if $495 interest was earned in 3 years at an interest rate of 6%.

$2,750

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Find the principal invested if $1,246 interest was earned in 5 years at an interest rate of 7% .

$3,560

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Now we will solve for the rate of interest.

Find the rate if a principal of $8,200 earned $3,772 interest in 4 years.

Solution

Organize the given information.

I = $3,772 P = $8,200 r = ? t = 4 years

We will use the simple interest formula to find the rate.

Write the formula. I = P r t
Substitute the given information. 3,772 = 8,200 r ( 4 )
Multiply. 3,772 = 32,800 r
Divide. 3,772 32,800 = 32,800 r 32,800
Simplify. 0.115 = r
Write as a percent. 11.5% = r
Check your answer. Is 11.5% a reasonable rate if $3,772 was earned in 4 years?
I = P r t
3,772 = ? 8,200 ( 0.115 ) ( 4 )
3,772 = 3,772
Write a complete sentence that answers the question. The rate was 11.5%.
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Questions & Answers

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Source:  OpenStax, Prealgebra. OpenStax CNX. Jul 15, 2016 Download for free at http://legacy.cnx.org/content/col11756/1.9
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